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Treat the buildings as fixed labelled objects

A developer has recently completed a condominium project in HCI Valley. There are 5 blocks of buildings A, B, C, D and E as shown. The developer has 4 colours available. Each block can only be painted using a single colour. Find the number of ways to paint all 5 blocks if

(i) there are no restrictions, mark

(ii) block A and block B cannot be painted with the same colour, marks

(iii) all 4 colours must be used. marks

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Block A is above, B upper right, C lower right, D lower left and E upper left, retaining the source pentagonal placement. These are five labelled fixed buildings, not interchangeable circular seats.
Block A is above, B upper right, C lower right, D lower left and E upper left, retaining the source pentagonal placement. These are five labelled fixed buildings, not interchangeable circular seats.
Block A is above, B upper right, C lower right, D lower left and E upper left, retaining the source pentagonal placement. These are five labelled fixed buildings, not interchangeable circular seats.

[2011/HCI/II/6]

CJC · Review problems · Question 8

All four colours on five buildings means exactly one colour occurs twice.

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